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Semigroup vs Commutant - What's the difference?

semigroup | commutant |

As nouns the difference between semigroup and commutant

is that semigroup is any set for which there is a binary operation that is both closed and associative while commutant is the subset of all elements of a semigroup that commute with the elements of a given subset.

semigroup

English

Noun

(wikipedia semigroup) (en noun)
  • (mathematics) Any set for which there is a binary operation that is both closed and associative.
  • * 1961 , Alfred Hoblitzelle Clifford, ?G. B. Preston, The Algebraic Theory of Semigroups (page 70)
    • If a semigroup S'' contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set ''K'' of all the zeroids of ''S'' is the kernel of ''S .

    Hyponyms

    * monoid * group

    commutant

    English

    Noun

    (en noun)
  • (algebra, logic) The subset of all elements of a semigroup that commute with the elements of a given subset
  • * {{quote-journal, year=2008, date=September 27, author=John Earman, title=Superselection Rules for Philosophers, work=Erkenntnis, doi=10.1007/s10670-008-9124-z, volume=69, issue=3, url=
    • , passage=The basic mathematical entity to be used here in elucidating the different senses of superselection rules is a von Neumann algebra {\mathfrak{M}}, a concrete C * -algebra 6 of bounded linear operators acting on a Hilbert space 7 {\mathcal{H}} that is closed in the weak topology 8 or, equivalently, 9 that has the property that ({\mathfrak{M}}^{\prime})^{\prime}:={\mathfrak{M}}^{\prime \prime }={\mathfrak{M}}, where “?” denotes the commutant .}}

    See also

    * (wikipedia "commutant") ----